There's the HITS Desert Circuit which is an annual horse show held at the HITS Desert Horse Park in Thermal not that far from Palm Springs. This year's dates are from Jan 26 until March 14. It's a horse show, but also offers classes and is open to the public to watch. I believe it's free.

1/26/10 - 3/14/10
The 20th Annual HITS Desert Circuit
HITS Desert Horse Park, 85-555 Airport Blvd., Thermal, CA / Six-week hunter/jumper horse show circuit produced by HITS, Inc. that runs from January through March annually. The Desert Circuit has been a mainstay of West Coast competition for the past 20 years and offers classes ranging from Grand Prix show jumping to a selection of divisions for both the novice and experienced rider. In addition, four of the 16 Grand Prix events at HITS Thermal are FEI World Cup Qualifiers. Total Grand Prix prize money offered for the 2010 season is nearly $1 million, which includes the $300,000 Grand Prix of the Desert. The HITS Desert Circuit is the winter show home to some of the most accomplished equestrian riders in the world, including U.S. Olympic Gold Medalist Will Simpson and Canadian Olympian Jill Henselwood. Grand Prix classes will be held on Sunday afternoons (1/31, 2/7, 2/14, 2/27, 3/7 and 3/14.) No admission charge Tues - Sat. Sunday admission is $5 per person, children under 12 are free. More info & schedule: 845.246.8833.